## wpiea2020290-print-pdf

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---

### Related literature and contribution
- Standstills are treated as a form of debt maturity extension and debt relief as debt restructuring; links to literature on optimal maturity choices in restructurings.
- Aguiar et al. (2019): optimal to shorten debt maturity in restructurings due to time-inconsistency (debt dilution) in default models with long-term debt (Arellano and Ramanarayanan, 2012; Chatterjee and Eyigungor, 2012, 2015; Hatchondo and Martinez, 2009; Hatchondo et al., 2020a, 2016; Sanchez et al., 2018).
- Dvorkin et al. (2020) and Mihalache (2020): explain observed maturity extensions by adding (i) risk of losing access to debt markets, (ii) a regulatory cost of haircuts, and (iii) restructurings after recovery. This paper differs by (a) modeling market access difficulty via an endogenous borrowing constraint, (b) not including regulatory haircut costs, and (c) focusing on preventive debt relief at the shock moment.
- Aguiar et al. (2019), Dvorkin et al. (2020), and Mihalache (2020) model bargaining and focus on restructurings that do not generate capital losses for creditors. This paper evaluates standstill proposals that could generate losses and studies improvements via haircuts.

- Mechanism emphasized here vs. prior work:
  - Prior: time-inconsistency leading to overindebtedness with long-term debt, raising optimality of shortening maturities at restructuring.
  - Here: standstills and haircuts move indebtedness in opposite directions.
    - Standstills increase indebtedness (automatic rollover), raising default probability and expected deadweight loss from defaults, thereby creating losses for creditors.
    - Haircuts lower indebtedness, reducing expected deadweight losses and creating gains for creditors.
  - Limiting borrowing through conditionality or fiscal rules mitigates time-inconsistency but does not mitigate shortcomings of standstills because debt issuances are not significant during standstills.
  - Combination of negative shocks and standstills creates opportunities for Pareto gains from haircuts.
  - If reluctance to use haircuts is due to regulation or doctrine of necessity, resulting inefficiencies are significant.
  - Losses from combining haircuts with a standstill are not always significant, and are less significant for larger haircuts.
  - Standstills can generate capital gains for creditors only when they prevent a default.

- Empirical context and supporting evidence (cited):
  - Jaramillo and Tejada (2011): spread more sensitive to increases in external public debt in countries without investment grade.
  - David et al. (2019): larger decline in spread after fiscal consolidation announcements when spread was already high.
  - Hatchondo et al. (2020a): spread increases more with debt in years with high spread.
  - Bi and Traum (2020); Gu and Stangebye (2018): fiscal information has more effect on bond prices during crises.
  - Historical recognition of Pareto improvements from resolving debt overhang (Froot, 1989; Krugman, 1988a; Krugman, 1988b; Sachs, 1989).

- Limitations noted in related literature:
  - Free-riding or holdout problem prevents individual creditors from accepting haircuts even if Pareto-improving for creditors as a group (Wright, 2011).
  - Analyzing why creditors (including official and multilateral) could accept capital losses or how losses could be imposed to private creditors is beyond the scope (Bolton et al., 2020 discussion on doctrine of necessity).

### Model setup and calibration (selected quantitative details)
- Preferences: E_t sum_{j=t}^{∞} β^{j−t} u(c_j); u(c) = (c^{1−γ} − 1)/(1−γ), with γ6= 1 (format preserved as in source).
- Bond structure: long-term bonds with coupon decay rate δ; debt dynamics b_{t+1} = (1−δ) b_t + l_t.
- Investors: risk-neutral foreign investors discount at risk-free rate r.
- Default features: exclusion from debt market for stochastic periods; income during exclusion y − φ(y); exit from default with constant probability ψ∈[0,1]; government exits default without debt.
- Markov process for endowment y; timing: government observes income, chooses default, then can change debt positions.

Selected benchmark parameter values:
- Risk aversion γ2 Standard
- Risk-free rate r1%
- Discount factor β0.9745 Standard
- Probability default ends ψ0.083 E(exclusion) = 3 years
- Debt duration δ0.033 Debt duration = 5 years
- Income autocorrelation coefficient ρ0.94 Mexico GDP
- Standard deviation of innovations σ1.5% Mexico GDP
- Mean log income μ(-1/2)σ2 Mexico GDP Calibrated to match targets
- Income cost of defaulting λ0 0.183 Average debt =44%
- Income cost of defaulting λ1 1.343 Average spread =3.4%

Notes on calibration:
- A period equals a quarter.
- ψ= 0.083 implies average duration of sovereign default events of three years.
- δ= 3.3% implies average bond duration of 5 years in simulations.
- Income cost parameters λ0 and λ1 calibrated to target average debt-to-GDP of 44 percent and mean spread of 3.4 percent.
- Simulations use value function iteration and interpolation; moments compared to Mexico data from Q1 1980 to Q4 2011 unless otherwise stated.

Business-cycle moments (selected exact values from Table 2):
- Targeted moments: Mean Debt-to-GDP 44 44; Mean spread (r_s) 3.4 3.4
- Non-targeted moments (Model vs Data):
  - σ(c)/σ(y) 1.4 1.2
  - σ(tb) 0.8 1.4
  - σ(r_s) 1.5 1.5
  - ρ(tb,y) -0.8 -0.7
  - ρ(c,y) 0.99 0.93
  - ρ(r_s,y) -0.7 -0.5
  - ρ(r_s,tb) 0.9 0.6

### Shock scenarios analyzed (exact specifications)
- Baseline economy starts at mean debt and endowment values and is hit by one of three baseline endowment shocks:
  - Small shock: sovereign spread increases by 250 basis points (y= 0.9681). Consistent with EMBI spread increase between December 2019 and April 2020 for economies preserving market access.
  - Large shock: sovereign spread increases by 1000 basis points (y= 0.9475). Represents shock faced by sub-investment grade borrowers; e.g., Sub-Saharan Africa average increase of 1,000 basis points with COVID-19.
  - Default shock: smallest shock that triggers default (y= 0.934); a standstill would prevent the default.
- Temporary shocks variant: mean income declines by χ for four quarters and recovers by χ/4 in next four quarters (back to benchmark in two years). For baseline spread criteria, χ = 5.7%, χ = 8.9%, and χ = 9.5% corresponding to small, large, and default baseline shocks respectively.
- Sudden-stop variant: baseline shocks plus constraint disallowing government borrowing during first four periods after the shock (models sudden stops).

### Standstill design (exact features)
- When shock period occurs, lenders and government enter a debt standstill agreement lasting for T_DS periods.
- During each of these T_DS periods, government is exempt from making debt payments and the stock of debt grows at rate r_DS.
- Government can issue debt during the standstill; payments of pre-standstill debt and new debt payments start after the standstill is over.
- A default ends the standstill.
- Assumed r_DS = 1.85%, equal to risk-free rate plus average (quarterly) spread; consistent with implementing standstills that do not produce present-value losses to creditors. (Analyzing different r_DS is equivalent to introducing haircuts.)

### Main quantitative findings on standstills vs haircuts
- Standstills yield sovereign welfare gains that increase with the standstill duration; welfare gains measured as equivalent per-period permanent consumption increase.
- Except when a standstill prevents a default, standstills generate capital losses for creditors. Creditors’ losses defined as decline in market value of debt holdings:
  - Without standstills: MV(b,y) = b [1 − ˆd(b,y)] [1 + (1−δ) q(ˆb(b,y),y)]
  - With a standstill: MV_DS_j(b,y) = b [1 − ˆd_DS_j(b,y)] (1 + r_DS) q_DS_j(ˆb_DS_j(b,y),y)
  - ˆd_DS_j, ˆq_DS_j, and ˆb_DS_j denote equilibrium functions in period j of the debt standstill.
- Two sources of creditors’ losses from standstills:
  1. Creditors not properly compensated for payments postponed during the standstill (postponed payments priced with r_DS which understates default risk after large negative shocks).
  2. Standstills increase debt levels, raising default probability after the standstill.
- Standstills can be difficult to implement voluntarily because private creditors may incur capital losses even before free-riding or holdout problems.
- Haircuts tend to be superior to standstills (consistent with Aguiar et al., 2019; Dvorkin et al., 2020; Mihalache, 2020), but mechanism differs: automatic rollover during standstills raises debt even if issuances are not significant.
- Relief from a standstill is short-lived; market access conditions unfavorable when government needs to start rolling over debt after the standstill (partly due to higher debt levels caused by the standstill). Government therefore does not want to increase indebtedness during the standstill.
- Losses from combining haircuts with a standstill are not always significant, and become less significant for larger haircuts.
- Standstills can generate capital gains for creditors only when they prevent a default.

### Combining standstills with haircuts — main findings
- Standstills (without haircuts) produce welfare gains for the sovereign but produce capital losses for creditors (except when they avoid a default).
- Introducing haircuts (reductions in nominal indebtedness) increases sovereign welfare and can generate capital gains for creditors even after shocks that would not trigger a default.
- Initial debt level is 44%.
- Standstills trigger a sovereign debt overhang: a debt reduction can increase repayment probability and market value of creditors’ debt holdings.
- Both a negative shock and a standstill contract the debt market value curve; after a standstill, the initial debt level can lie in the declining portion of the market value curve even for a small shock, creating room for haircuts that increase market value.
- The hump shape of the debt market value curves implies capital losses (or gains) triggered by haircuts are non-monotonic with respect to haircut size.

- Agreement and disagreement zones (baseline large shock with one-year standstill):
  - Agreement zone: haircuts up to 21% — both sovereign and creditors (as a group) benefit from higher haircuts. Any haircut lower than 21%, including the standstill without a haircut, would be an inefficient debt relief from sovereign welfare and creditors’ capital losses perspective.
  - Disagreement zone: haircuts between 21% and 47% — sovereign prefers higher haircuts, lenders prefer lower haircuts, but lenders still have capital gains from these haircuts compared with standstill-only debt relief. This disagreement zone includes all possible efficient outcomes of a debt relief with a one-year standstill.
  - Creditors’ losses occur only for haircuts higher than 47% in addition to those triggered by the standstill.

- Comparative performance:
  - Except when incorporating the sudden stop shock, haircuts dominate standstills as instruments of debt relief: for any level of capital losses that could be imposed on creditors, implementing debt relief only with a haircut produces a larger welfare gain than combining the haircut with a standstill.
  - After large shocks, haircuts can achieve simultaneously capital gains for creditors and welfare gains for the sovereign. This cannot be achieved with standstills alone and is more difficult when combining standstills with haircuts.
  - With sudden stop shocks (when government cannot borrow), a standstill might be expected to be more adequate; however, haircuts retain a significant comparative advantage: adding a standstill to haircuts can only improve welfare slightly, and does so only for haircuts of more than 30% (even assuming the debt reduction implied by haircuts does not improve market access during the sudden stop).

- Mechanism:
  - Haircuts reduce indebtedness and thus lower default probability.
  - Standstills increase indebtedness and default probability.
  - Haircuts lower expected deadweight losses from defaults and create creditors’ gains; standstills increase expected deadweight losses and create creditors’ losses.
  - Appendix B presents a stylized model illustrating this mechanism.

- Efficiency of combining large haircuts with standstills:
  - Losses from combining haircuts with a standstill are not always significant and are less significant for debt reliefs that include large haircuts.
  - Example (baseline large shock, one-year standstill): without haircuts the one-year standstill would trigger a 21% capital loss. For this loss, inefficiency of combining haircuts with a one-year standstill is negligible: almost the same welfare gain can be obtained with either a 47.3% haircut alone or combining a 47.1% haircut with a one-year standstill. For low debt levels implied by such large haircuts, the standstill is not expected to produce a significant increase in indebtedness.

### Dynamics after the shock — simulation evidence
- Simulation setups (baseline large shock; only non-zero shock) — five scenarios:
  - (i) without debt relief,
  - (ii) with a one-year standstill only,
  - (iii) with the one-year standstill and the 20.9% haircut that minimizes creditor losses given the standstill,
  - (iv) with the one-year standstill and the 47.1% haircut that maximizes the government’s gains without additional creditor losses given the standstill,
  - (v) without standstill and with the 47.3% haircut that produces the same capital losses as option (iv).

- Impulse-response results and key statistics:
  - The standstill worsens government’s market access: on top of spread increase because of the shock, the spread increases by an additional 800 basis points because of the standstill, and is higher than without debt relief throughout the projection period.
  - Higher post-standstill spreads reflect higher post-standstill default probabilities despite lower default probabilities during the standstill; higher default probabilities explained by higher debt levels.
  - While issuances are lower with the standstill, debt levels are higher because of debt automatically rolled over during the standstill.
  - Net borrowing (borrowing net of debt payments) is higher during the standstill even though borrowing is lower during the standstill.

- Consumption, spreads, and market value outcomes:
  - During the year of the standstill, all debt relief alternatives mitigate significantly the drop in consumption triggered by the shock.
  - By itself, the standstill reduces consumption in every period after the first year because of poor borrowing conditions and larger net debt payments (more negative net borrowing) after the standstill.
  - Combining the standstill with the 20.9% haircut: consumption is even higher during the standstill, and is significantly higher than without debt relief throughout the projection period; spreads are significantly lower, and the debt market value is close to the one without debt relief. The haircut eliminates the debt overhang created by the negative shock and the standstill.
  - A one-year standstill with a 47.1% haircut and a 47.3% haircut without a standstill generate almost identical paths for the debt level and the spread (and thus for the debt market value), similar paths for consumption, and almost identical welfare gains for the sovereign.

### Conclusions (excerpted)
- Findings cast doubts on emphasis on sovereign debt standstills without haircuts as best alternative for providing debt relief to countries suffering because of COVID-19.
- Standstills produce a sovereign debt overhang and thus create opportunity for voluntary debt exchanges: adding haircuts to standstills can improve government’s welfare while lowering creditors’ losses.
- If emphasis on standstills without haircuts is driven by regulatory costs of reductions in nominal debt value or doctrine of necessity, these legal frameworks could create significant inefficiencies in debt relief outcomes.

### Appendix A — Positive recovery: model variant and robustness
- Default does not extinguish debt: after default, debt equals fraction of mean debt in simulations.
- Recovered debt level: b_D = min{α, b}.
- Recursive value functions:
  - V(b,y) = max_{d∈{0,1}} { d V1(b,y) + (1−d) V0(b,y) }.
  - V1(b,y) = u(y−φ(y)) + β ∫ [ ψ V(b_D, y′) + (1−ψ) V1(b_D, y′) ] F(dy′|y).
  - V0(b,y) = max_{b′ ≥ 0} { u(y − b + q(b′, y) [ b′ − (1−δ) b ]) + β ∫ V(b′, y′) F(dy′|y) }, subject to b′ > (1−δ) b only if q(b′, y) > q.
- Bond pricing incorporates recovery:
  - q(b′, y) = (1/(1 + r)) ∫ [1 − \^d(b′, y′)] [1 + (1−δ) q(\^b(b′, y′), y′)] F(dy′|y) + (1/(1 + r)) ∫ \^d(b′, y′) q_D(b′, y′) F(dy′|y).
  - q_D(b, y) defined recursively as price of a bond in default.
- Constraint on bond issuance price q prevents infinite pre-default issuance; choose q such that (i) eliminates consumption booms before defaults, (ii) is never binding in simulations, and (iii) allows debt issuances at sovereign spread levels observed in the data.

- Calibration and model fit (new parameters):
  - Price floor: q = 0.5/(r + δ), ensuring q never binding in simulations and implies government cannot issue debt at a price lower than 50% of risk-free price.
  - Recovered debt parameter: α = 0.62, which amounts to 35% of mean debt and consistent with average haircut of 65% reported by Cruces and Trebesch (2013).
- Recalibrated income cost of defaulting to match targeted moments:
  - λ0 and λ1 chosen to match average debt-to-GDP ratio of 44 percent and mean spread of 3.4 percent.

- Parameter values (as reported):
  - Risk aversion γ: 2 Standard
  - Risk-free rate r: 1% Standard
  - Discount factor β: 0.9745 Standard
  - Probability default ends ψ: 0.083 E(exclusion) = 3 years
  - Debt duration δ: 0.033 Debt duration = 5 years
  - Income autocorrelation coefficient ρ: 0.94 Mexico GDP
  - Standard deviation of innovations σ_ε: 1.5% Mexico GDP
  - Mean log income μ: (-1/2) σ^2_ε Mexico GDP
  - Price floor q: 0.5/(δ + r) never binding
  - Recovered debt α: 0.62 35% recovery rate
  - Income cost of defaulting λ0: 0.15 Average debt = 44%
  - Income cost of defaulting λ1: 1.33 Average spread = 3.4%

- Model match to moments (Table A.2):
  - Targeted: Mean Debt-to-GDP: Model (w/ recovery) 44 ; Data 44
  - Mean r_s: Model (w/ recovery) 3.4 ; Data 3.4
  - Non-targeted:
    - σ(c)/σ(y): Model 1.3 ; Data 1.2
    - σ(tb): Model 0.6 ; Data 1.4
    - σ(r_s): Model 1.3 ; Data 1.5
    - ρ(tb,y): Model -0.8 ; Data -0.7
    - ρ(c,y): Model 0.99 ; Data 0.93
    - ρ(r_s,y): Model -0.8 ; Data -0.5
    - ρ(r_s,tb): Model 0.7 ; Data 0.6

- Robustness of main results (positive recovery):
  - Shock definitions (temporary drops of mean income):
    - “Small” shock: increases spread by 250 bps (3.6% decline of mean income).
    - “Large” shock: increases spread by 1000 bps (7.1% decline).
    - “Default” shock: smallest decline that triggers a default without standstills (7.6%).
  - Main findings remain:
    - Standstills produce sovereign welfare gains but, except when avoiding defaults, produce capital losses for lenders.
    - Capital losses from standstill can be mitigated with haircuts that also increase sovereign welfare.
    - Using only haircuts continues to be best form of debt relief; losses from combining haircuts with a standstill are less significant for larger haircuts.
    - For larger shocks in positive-recovery specification, haircuts do not mitigate significantly capital losses triggered by the 3 years standstill because expected increase in indebtedness during the 3 years standstill undoes positive effect of haircuts on default probability; nonetheless, haircuts still significantly increase sovereign welfare gains, and the 3 years standstill is strongly Pareto dominated by other forms of debt relief.

- Debt market value expressions:
  - Without standstills: MV(b,y) = b [1 − \^d(b,y)] [1 + (1−δ) q(\^b(b,y), y)] + b_D \^d(b,y) q_D(b_D, y).
  - With standstills (policy j): MV_DS_j(b,y) = b [1 − \^d_DS_j(b,y)] (1 + r_DS) q_DS_j(\^b_DS_j(b,y), y) ] + b_D \^d_DS_j(b,y) q_D(b_D, y).

### Appendix B — Two-period model: intuition for haircuts vs standstills
- Environment:
  - Two periods (1 and 2), borrower and lenders risk neutral, borrower discount factor β.
  - Initial debt b > 0 consists of legacy bonds paying coupon δ in period 1 and principal 1 in period 2.
  - No new issuance (sudden stop) and no income; default only possible in period 2.
  - Stochastic default cost φ with pdf f and cdf F; f continuous.

- Value under repayment:
  - Borrower defaults in period 2 if b > φ.
  - Continuation value in period 1: V(b) = −δ b − β [1 − F(b)] b − β ∫_{−∞}^{b} φ f(φ) dφ.
  - Bond price at beginning of period 1: q(b) = δ + 1 − F(b).

- Standstill (postponing δ b coupons due in period 1):
  - V_S(b) = −β [1 − F(b(1 + δ))] b(1 + δ) − β ∫_{−∞}^{b(1 + δ)} φ f(φ) dφ.
  - q_S(b) = [1 − F(b(1 + δ))] (1 + δ).

- Proposition 1 (standstill effects):
  - For all b: V_S(b) > V(b) and q_S(b) < q(b).
  - Interpretation: borrower strictly better off with standstill; bondholders strictly worse off. Standstill swaps a sure near-term repayment for a less-certain, discounted later repayment and increases default probability by increasing indebtedness.

- Haircut:
  - If haircut reduces initial debt to \^b < b then V(\^b) > V(b) and q(\^b) > q(b).

- Proposition 2 (existence of Pareto-improving haircut):
  - For any initial debt b, there exists β(b) such that for all β ∈ [β(b), 1], there is a haircut \^b < b such that V(\^b) > V_S(b) and q(\^b) \^b > q_S(b) b.
  - Intuition: with sufficiently patient borrower (high β), a haircut can reduce default probability and deadweight default cost enough that both borrower and bondholders prefer the haircut to a standstill.

- Key analytic expression:
  - V(b) − V_S(b) = δ b (β − 1) + β ∫_{b}^{b(1 + δ)} φ f(φ) dφ. This expression is continuous and strictly increasing in β, negative at β = 0 and positive at β = 1, implying existence of β(b) ∈ (0,1) where V(b) ≥ V_S(b) for β ∈ [β(b), 1].

*Source: wpiea2020290-print-pdf — 3.2 Combining standstills with haircuts (IMF Working Paper).*

### 1.1    Related literature

### 1.1    Related literature

### Relation to existing studies
- Standstills are treated as a form of debt maturity extension and debt relief as debt restructuring, linking this analysis to literature on optimal maturity choices in restructurings.
- Aguiar et al. (2019): show it is optimal to shorten debt maturity in debt restructurings due to a time-inconsistency (debt dilution) problem in default models with long-term debt (Arellano and Ramanarayanan, 2012; Chatterjee and Eyigungor, 2012, 2015; Hatchondo and Martinez, 2009; Hatchondo et al., 2020a, 2016; Sanchez et al., 2018).
- Dvorkin et al. (2020) and Mihalache (2020): explain observed maturity extensions by adding (i) risk of losing access to debt markets, (ii) a regulatory cost of haircuts, and (iii) restructurings after recovery. This paper differs by (a) modeling market access difficulty via an endogenous borrowing constraint, (b) not including regulatory haircut costs, and (c) focusing on preventive debt relief at the shock moment.
- Aguiar et al. (2019), Dvorkin et al. (2020), and Mihalache (2020) model bargaining and focus on restructurings that do not generate capital losses for creditors. This paper evaluates standstill proposals that could generate losses and studies improvements via haircuts.

### Mechanisms emphasized here vs. prior work
- Prior literature emphasizes time-inconsistency leading to overindebtedness with long-term debt; this raises optimality of shortening maturities at restructuring.
- This paper emphasizes a different mechanism: standstills and haircuts move indebtedness in opposite directions.
  - Standstills increase indebtedness (automatic rollover), raising default probability and expected deadweight loss from defaults, thereby creating losses for creditors.
  - Haircuts lower indebtedness, reducing expected deadweight losses and creating gains for creditors.
- Limiting borrowing through conditionality or fiscal rules mitigates time-inconsistency but does not mitigate the shortcomings of standstills because debt issuances are not significant during standstills.
- Combination of negative shocks and standstills creates opportunities for Pareto gains from haircuts.
- If reluctance to use haircuts is due to regulation or doctrine of necessity, the resulting inefficiencies are significant.
- Losses from combining haircuts with a standstill are not always significant, and are less significant for larger haircuts.

### Empirical context and supporting evidence (as cited)
- Jaramillo and Tejada (2011): spread more sensitive to increases in external public debt in countries without investment grade.
- David et al. (2019): larger decline in spread after fiscal consolidation announcements when spread was already high.
- Hatchondo et al. (2020a): spread increases more with debt in years with high spread.
- Bi and Traum (2020); Gu and Stangebye (2018): fiscal information has more effect on bond prices during crises.
- Historical recognition of Pareto improvements from resolving debt overhang (Froot, 1989; Krugman, 1988a; Krugman, 1988b; Sachs, 1989).

### Limitations noted in related literature
- Free-riding or holdout problem prevents individual creditors from accepting haircuts even if they are Pareto-improving for creditors as a group (Wright, 2011).
- Analyzing why creditors (including official and multilateral) could accept capital losses or how losses could be imposed to private creditors is beyond the scope of this paper (Bolton et al., 2020 offers discussion on the doctrine of necessity).

---

### Model setup and calibration (selected quantitative details)
- Preferences: E_t sum_{j=t}^{∞} β^{j−t} u(c_j); utility displays constant coefficient of relative risk aversion u(c) = (c^{1−γ} − 1)/(1−γ), with γ6= 1 (format preserved as in source).
- Bond structure: long-term bonds with coupon decay rate δ; debt dynamics b_{t+1} = (1−δ) b_t + l_t.
- Investors: risk-neutral foreign investors discount at risk-free rate r.
- Default features: exclusion from debt market for stochastic periods; income during exclusion y − φ(y); exit from default with constant probability ψ∈[0,1]; government exits default without debt.
- Markov process for endowment y; timing: government observes income, chooses default, then can change debt positions.

Selected benchmark parameter values (as presented):
- Risk aversion γ2 Standard
- Risk-free rate r1%
- Discount factor β0.9745 Standard
- Probability default ends ψ0.083 E(exclusion) = 3 years
- Debt duration δ0.033 Debt duration = 5 years
- Income autocorrelation coefficient ρ0.94 Mexico GDP
- Standard deviation of innovations σ1.5% Mexico GDP
- Mean log income μ(-1/2)σ2 Mexico GDP Calibrated to match targets
- Income cost of defaulting λ0 0.183 Average debt =44%
- Income cost of defaulting λ1 1.343 Average spread =3.4%

Notes on calibration:
- A period equals a quarter.
- ψ= 0.083 implies average duration of sovereign default events of three years.
- δ= 3.3% implies average bond duration of 5 years in simulations.
- Income cost parameters λ0 and λ1 are calibrated to target average debt-to-GDP of 44 percent and mean spread of 3.4 percent.
- Simulations use value function iteration and interpolation; moments are compared to Mexico data from Q1 1980 to Q4 2011 unless otherwise stated.

Business-cycle moments (selected exact values from Table 2):
- Targeted moments: Mean Debt-to-GDP 44 44 (ModelData columns show 44 and 44); Mean spread (r_s) 3.4 3.4
- Non-targeted moments (Model vs Data):
  - σ(c)/σ(y) 1.4 1.2
  - σ(tb) 0.8 1.4
  - σ(r_s) 1.5 1.5
  - ρ(tb,y) -0.8 -0.7
  - ρ(c,y) 0.99 0.93
  - ρ(r_s,y) -0.7 -0.5
  - ρ(r_s,tb) 0.9 0.6

---

### Shock scenarios analyzed (exact specifications)
- Baseline economy starts at mean debt and endowment values in simulations and is hit by one of three baseline endowment shocks:
  - Small shock: sovereign spread increases by 250 basis points (y= 0.9681). Consistent with EMBI spread increase between December 2019 and April 2020 for economies preserving market access.
  - Large shock: sovereign spread increases by 1000 basis points (y= 0.9475). Represents shock faced by sub-investment grade borrowers; e.g., Sub-Saharan Africa average increase of 1,000 basis points with COVID-19.
  - Default shock: smallest shock that triggers default (y= 0.934); a standstill would prevent the default.
- Temporary shocks variant: mean income declines by χ for four quarters and recovers by χ/4 in next four quarters (back to benchmark in two years). For baseline spread criteria, χ = 5.7%, χ = 8.9%, and χ = 9.5% corresponding to small, large, and default baseline shocks respectively.
- Sudden-stop variant: baseline shocks plus constraint disallowing government borrowing during first four periods after the shock (models sudden stops).

---

### Standstill design (exact features)
- When shock period occurs, lenders and government enter a debt standstill agreement lasting for T_DS periods.
- During each of these T_DS periods, government is exempt from making debt payments and the stock of debt grows at rate r_DS.
- Government can issue debt during the standstill; payments of pre-standstill debt and new debt payments start after the standstill is over.
- A default ends the standstill.
- Assumed r_DS = 1.85%, equal to risk-free rate plus average (quarterly) spread; consistent with implementing standstills that do not produce present-value losses to creditors. (Analyzing different r_DS is equivalent to introducing haircuts.)

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### Main quantitative findings on standstills vs haircuts
- Standstills yield sovereign welfare gains that increase with the standstill duration. Welfare gains are measured as the equivalent per-period permanent consumption increase.
- Except when a standstill prevents a default, standstills generate capital losses for creditors. Creditors’ losses are defined as the decline in the market value of debt holdings:
  - Without standstills: MV(b,y) = b [1 − ˆd(b,y)] [1 + (1−δ) q(ˆb(b,y),y)]
  - With a standstill: MV_DS_j(b,y) = b [1 − ˆd_DS_j(b,y)] (1 + r_DS) q_DS_j(ˆb_DS_j(b,y),y)
  - Here ˆd_DS_j, ˆq_DS_j, and ˆb_DS_j denote the equilibrium functions in period j of the debt standstill.
- Two sources of creditors’ losses from standstills:
  1. Creditors are not properly compensated for payments postponed during the standstill (postponed payments priced with r_DS which understates default risk after large negative shocks).
  2. Standstills increase debt levels, raising default probability after the standstill.
- Standstills can be difficult to implement voluntarily because, despite sovereign benefits, private creditors may incur capital losses even before considering free-riding or holdout problems.
- Haircuts tend to be superior to standstills (consistent with Aguiar et al., 2019; Dvorkin et al., 2020; Mihalache, 2020), but the underlying mechanism differs: here, automatic rollover during standstills raises debt even if issuances are not significant.
- Relief from a standstill is short-lived in this model, and market access conditions are unfavorable when the government needs to start rolling over debt after the standstill (partly due to higher debt levels caused by the standstill). Therefore, the government does not want to increase indebtedness during the standstill.
- Losses from combining haircuts with a standstill are not always significant, and become less significant for larger haircuts.
- Standstills can generate capital gains for creditors only when they prevent a default.

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*wpiea2020290-print-pdf - 1.1    Related literature*

### 3.2    Combining standstills with haircuts

### 3.2    Combining standstills with haircuts

### Main findings on welfare and capital gains/losses
- Standstills (without haircuts) produce welfare gains for the sovereign but produce capital losses for creditors (except when they avoid a default).
- Introducing haircuts (reductions in the nominal level of indebtedness) increases sovereign welfare and, in contrast with standstills, can generate capital gains for creditors even after shocks that would not trigger a default.
- Initial debt level is 44%.
- Standstills trigger a sovereign debt overhang: a debt reduction can increase the probability of repayment and the market value of creditors’ debt holdings.
- Both a negative shock and a standstill contract the debt market value curve; after a standstill, the initial debt level can lie in the declining portion of the market value curve even for a small shock, creating room for haircuts that increase market value.
- The hump shape of the debt market value curves implies that capital losses (or gains) triggered by haircuts are non-monotonic with respect to the size of the haircut.

### Agreement and disagreement zones (baseline large shock with one-year standstill)
- Agreement zone: haircuts up to 21% — both the sovereign and creditors (as a group) benefit from higher haircuts. Any haircut lower than 21%, including the standstill without a haircut, would be an inefficient debt relief from the perspective of the sovereign’s welfare and the creditor’s capital losses.
- Disagreement zone: haircuts between 21% and 47% — the sovereign prefers higher haircuts, lenders prefer lower haircuts, but lenders still have capital gains from these haircuts compared with the standstill-only debt relief. This disagreement zone includes all possible efficient outcomes of a debt relief with a one-year standstill.
- Creditors’ losses occur only for haircuts higher than 47% in addition to those triggered by the standstill.

### Comparative performance of haircuts vs. standstills
- Except when incorporating the sudden stop shock, haircuts dominate standstills as instruments of debt relief: for any level of capital losses that could be imposed on creditors, implementing debt relief only with a haircut produces a larger welfare gain than combining the haircut with a standstill.
- After the large shocks, haircuts can achieve simultaneously capital gains for creditors and welfare gains for the sovereign. This cannot be achieved with standstills alone and is more difficult when combining standstills with haircuts.
- With sudden stop shocks (when the government cannot borrow), a standstill might be expected to be more adequate; however, haircuts still retain a significant comparative advantage: adding a standstill to haircuts can only improve welfare slightly, and does so only for haircuts of more than 30% (even assuming the debt reduction implied by haircuts does not improve market access during the sudden stop).

### Mechanism: why haircuts dominate
- Haircuts reduce indebtedness and thus lower the default probability.
- Standstills increase indebtedness and the default probability (Figure 3).
- Haircuts tend to lower expected deadweight losses from defaults and create creditors’ gains; standstills tend to increase expected deadweight losses from defaults and create creditors’ losses.
- Appendix B presents a stylized model illustrating this mechanism.

### Efficiency of combining large haircuts with standstills
- Losses from combining haircuts with a standstill are not always significant and are less significant for debt reliefs that include large haircuts.
- Example (baseline large shock, one-year standstill): without haircuts the one-year standstill would trigger a 21% capital loss. For this loss, the inefficiency of combining haircuts with a one-year standstill is negligible: almost the same welfare gain can be obtained with either a 47.3% haircut alone or combining a 47.1% haircut with a one-year standstill. For the low debt levels implied by such large haircuts, the standstill is not expected to produce a significant increase in indebtedness.

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### 3.3    Dynamics after the shock

### Simulation setups (baseline large shock; only non-zero shock)
Five sets of simulations considered:
- (i) without debt relief,
- (ii) with a one-year standstill only,
- (iii) with the one-year standstill and the 20.9% haircut that minimizes creditor losses given the standstill,
- (iv) with the one-year standstill and the 47.1% haircut that maximizes the government’s gains without additional creditor losses given the standstill,
- (v) without standstill and with the 47.3% haircut that produces the same capital losses as option (iv).

### Impulse-response results and key statistics
- The standstill worsens the government’s market access: on top of the spread increase because of the shock, the spread increases by an additional 800 basis points because of the standstill, and is higher than without debt relief throughout the projection period.
- Higher post-standstill spreads reflect higher post-standstill default probabilities in spite of lower default probabilities during the standstill; higher default probabilities are explained by higher debt levels.
- While issuances are lower with the standstill, debt levels are higher because of the debt that is automatically rolled over during the standstill.
- Net borrowing (borrowing net of debt payments) is higher during the standstill even though borrowing is lower during the standstill.

### Consumption, spreads, and market value outcomes
- During the year of the standstill, all debt relief alternatives mitigate significantly the drop in consumption triggered by the shock.
- By itself, the standstill reduces consumption in every period after the first year because of poor borrowing conditions and larger net debt payments (more negative net borrowing) after the standstill.
- Combining the standstill with the 20.9% haircut: consumption is even higher during the standstill, and is significantly higher and higher than without debt relief throughout the projection period; spreads are significantly lower, and the debt market value is close to the one without debt relief. The haircut eliminates the debt overhang created by the negative shock and the standstill.
- A one-year standstill with a 47.1% haircut and a 47.3% haircut without a standstill generate almost identical paths for the debt level and the spread (and thus for the debt market value), similar paths for consumption, and almost identical welfare gains for the sovereign.

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### 4    Conclusions (excerpted)
- The findings cast doubts on the emphasis on sovereign debt standstills without haircuts as the best alternative for providing debt relief to countries suffering because of COVID-19.
- Standstills produce a sovereign debt overhang and thus create the opportunity for voluntary debt exchanges: adding haircuts to standstills can improve the government’s welfare while lowering creditors’ losses.
- If emphasis on standstills without haircuts is driven by regulatory costs of reductions in the nominal value of debt holdings or by the doctrine of necessity, these legal frameworks could create significant inefficiencies in debt relief outcomes.

*Source: wpiea2020290-print-pdf — 3.2 Combining standstills with haircuts (IMF Working Paper).*

### 2011.  In Sovereign Debt and the Financial Crisis:  Will This Time Be Different?, eds. Carlos A. Primo Braga

### Appendix A — A positive recovery rate

### Model formulation and key assumptions
- Default does not extinguish debt: after a default event, debt is equal to a fraction of the mean debt in the simulations.
- Recovered debt level: b_D = min{α, b}.
- Recursive value functions:
  - V(b,y) = max_{d∈{0,1}} { d V1(b,y) + (1−d) V0(b,y) }.
  - V1(b,y) = u(y−φ(y)) + β ∫ [ ψ V(b_D, y′) + (1−ψ) V1(b_D, y′) ] F(dy′|y).
  - V0(b,y) = max_{b′ ≥ 0} { u(y − b + q(b′, y) [ b′ − (1−δ) b ]) + β ∫ V(b′, y′) F(dy′|y) }, subject to b′ > (1−δ) b only if q(b′, y) > q.
- Bond pricing incorporates recovery:
  - q(b′, y) = (1/(1 + r)) ∫ [1 − \^d(b′, y′)] [1 + (1−δ) q(\^b(b′, y′), y′)] F(dy′|y) + (1/(1 + r)) ∫ \^d(b′, y′) q_D(b′, y′) F(dy′|y).
  - q_D(b, y) defined recursively as the price of a bond in default.
- Constraint on bond issuance price q prevents infinite pre-default issuance that would dilute prior claims; choose q such that (i) eliminates consumption booms before defaults, (ii) is never binding in simulations, and (iii) allows debt issuances at sovereign spread levels observed in the data.

### Calibration and model fit
- New parameters to assign: α and q.
  - Price floor: q = 0.5/(r + δ), ensuring q is never binding in simulations and implies government cannot issue debt at a price lower than 50% of the risk-free price.
  - Recovered debt parameter: α = 0.62, which amounts to 35% of the mean debt in the simulations and is consistent with the average haircut of 65% reported by Cruces and Trebesch (2013) for reductions in face value.
- Recalibrated income cost of defaulting to match targeted moments:
  - λ0 and λ1 chosen to match an average debt-to-GDP ratio of 44 percent and a mean spread of 3.4 percent.
- Parameter values (as reported):
  - Risk aversion γ: 2 Standard
  - Risk-free rate r: 1% Standard
  - Discount factor β: 0.9745 Standard
  - Probability default ends ψ: 0.083 E(exclusion) = 3 years
  - Debt duration δ: 0.033 Debt duration = 5 years
  - Income autocorrelation coefficient ρ: 0.94 Mexico GDP
  - Standard deviation of innovations σ_ε: 1.5% Mexico GDP
  - Mean log income μ: (-1/2) σ^2_ε Mexico GDP
  - Price floor q: 0.5/(δ + r) never binding
  - Recovered debt α: 0.62 35% recovery rate
  - Income cost of defaulting λ0: 0.15 Average debt = 44%
  - Income cost of defaulting λ1: 1.33 Average spread = 3.4%

- Model match to targeted and non-targeted moments (Table A.2):
  - Targeted moments:
    - Mean Debt-to-GDP: Model (w/ recovery) 44 ; Data 44
    - Mean r_s: Model (w/ recovery) 3.4 ; Data 3.4
  - Non-targeted moments:
    - σ(c)/σ(y): Model 1.3 ; Data 1.2
    - σ(tb): Model 0.6 ; Data 1.4
    - σ(r_s): Model 1.3 ; Data 1.5
    - ρ(tb,y): Model -0.8 ; Data -0.7
    - ρ(c,y): Model 0.99 ; Data 0.93
    - ρ(r_s,y): Model -0.8 ; Data -0.5
    - ρ(r_s,tb): Model 0.7 ; Data 0.6

### Robustness of main results (positive recovery)
- Shock definitions (temporary drops of mean income):
  - “Small” shock: increases spread by 250 bps (3.6% decline of mean income).
  - “Large” shock: increases spread by 1000 bps (7.1% decline).
  - “Default” shock: smallest decline that triggers a default without standstills (7.6%).
- Main empirical/quantitative findings:
  - Standstills produce welfare gains for the sovereign but, except when they avoid a default, they produce capital losses for lenders.
  - Capital losses triggered by a standstill can be mitigated with haircuts that also increase sovereign welfare.
  - Using only haircuts continues to be the best form of debt relief; losses from combining haircuts with a standstill are less significant for larger haircuts.
  - For larger shocks in the positive-recovery specification, haircuts do not mitigate significantly the capital losses triggered by the 3 years standstill because the expected increase in indebtedness during the 3 years standstill undoes the positive effect of haircuts on default probability; nonetheless, haircuts can still significantly increase sovereign welfare gains, and the 3 years standstill is strongly Pareto dominated by other forms of debt relief.

- Debt market value expressions (as given):
  - Without standstills: MV(b,y) = b [1 − \^d(b,y)] [1 + (1−δ) q(\^b(b,y), y)] + b_D \^d(b,y) q_D(b_D, y).
  - With standstills (policy j): MV_DS_j(b,y) = b [1 − \^d_DS_j(b,y)] (1 + r_DS) q_DS_j(\^b_DS_j(b,y), y) ] + b_D \^d_DS_j(b,y) q_D(b_D, y).

### Appendix B — A two-period model: intuition for haircuts vs. standstills
- Environment and setup:
  - Two periods (1 and 2), borrower and lenders risk neutral, borrower discount factor β.
  - Initial debt b > 0 consists of legacy bonds paying coupon δ in period 1 and principal 1 in period 2.
  - No new issuance (sudden stop) and no income; default only possible in period 2.
  - Stochastic default cost φ with pdf f and cdf F; f continuous.
- Value under repayment:
  - Borrower defaults in period 2 if b > φ.
  - Continuation value in period 1: V(b) = −δ b − β [1 − F(b)] b − β ∫_{−∞}^{b} φ f(φ) dφ.
- Bond price at beginning of period 1:
  - q(b) = δ + 1 − F(b).
- Standstill (postponing δ b coupons due in period 1):
  - V_S(b) = −β [1 − F(b(1 + δ))] b(1 + δ) − β ∫_{−∞}^{b(1 + δ)} φ f(φ) dφ.
  - q_S(b) = [1 − F(b(1 + δ))] (1 + δ).

- Proposition 1 (standstill effects):
  - For all b: V_S(b) > V(b) and q_S(b) < q(b).
  - Interpretation: borrower strictly better off with standstill; bondholders strictly worse off. Standstill swaps a sure near-term repayment for a less-certain, discounted later repayment and increases default probability by increasing indebtedness.

- Haircut:
  - If haircut reduces initial debt to \^b < b then V(\^b) > V(b) and q(\^b) > q(b).
  - Proposition 2 (existence of Pareto-improving haircut):
    - For any initial debt b, there exists β(b) such that for all β ∈ [β(b), 1], there is a haircut \^b < b such that V(\^b) > V_S(b) and q(\^b) \^b > q_S(b) b.
    - Intuition: with sufficiently patient borrower (high β), a haircut can reduce default probability and deadweight default cost enough that both borrower and bondholders prefer the haircut to a standstill. Standstills raise indebtedness and default probability; haircuts reduce indebtedness and default probability.

- Key analytic expression (difference in borrower value between no-standstill and standstill for a particular b):
  - V(b) − V_S(b) = δ b (β − 1) + β ∫_{b}^{b(1 + δ)} φ f(φ) dφ. This expression is continuous and strictly increasing in β, negative at β = 0 and positive at β = 1, implying the existence of β(b) ∈ (0,1) where V(b) ≥ V_S(b) for β ∈ [β(b), 1].

*Source: wpiea2020290-print-pdf — Appendix A and Appendix B (2011).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020290-print-pdf.pdf_